• The Knight's Tour Problem and Rudrata's Verse

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/reso/025/08/1095-1116

    • Keywords

       

      Knight’s Tour Problem, Rudraṭa, cit-rakāvyam, turaṅga-padam, Sanskrit literature, cyclic permutation.

    • Abstract

       

      If a chess-knight is moved on a vacant chess-board [8 × 8 square] such that it visits each one of the 64 squares once and once only, the knight is said to execute a Knight’s Tour. Solution to the knight’s tour problem was known in India as early as the 9th century AD as a demonstration of wizardry in composing 32-syllable verses in Sanskrit. A pair of meaningful verses is composed in such a manner that when one verse is written serially (left to right and top to bottom) one syllable a square to fill up 8 × 4 cells — half of a chess board – the other verse appears as the Knight’s Tour. The earliest example of this skill in poetry-composition is given in a Sanskrit treatise on poetics, kāvyālaṅkāra written by Rudraṭa who lived around the ninth century A.D. Knight’s Tour as a mathematical problem was first noticed and discussed in the West by Leonard Euler in the eighteenth century. After providing the back ground to the subject as a puzzle on the chess-board, a problem in mathemat-ics and as a challenge in verse-composition, the article discusses the special characteristic of Rudrata’s example where the pair of verses reduces to a single verse.

    • Author Affiliations

       

      Murthy G S S1

      1. No.491, 7th cross 4th main JP Nagar 3rd phase Bangalore 560078
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